Covariance and crossover matrix guided differential evolution for global numerical optimization.

Area of Science:

• Computational Intelligence
• Optimization Algorithms
• Evolutionary Computation

Background:

• Differential Evolution (DE) is a powerful evolutionary algorithm widely used in science and engineering.
• Standard DE implementations face complexity due to diverse mutation/crossover strategies and parameter tuning.
• Existing DE variants often require intricate parameter settings for different evolutionary stages.

Purpose of the Study:

• To develop a novel, efficient, and simple DE variant (CCDE) with improved mutation and crossover operations.
• To enhance the exploration and exploitation capabilities of the DE algorithm.
• To improve population diversity and overall optimization performance.

Main Methods:

• Introduced a crossover matrix to replace the traditional crossover operator and its control parameter (CR).
• Utilized Gaussian distribution centered by a covariance matrix derived from elite individuals for population refinement.
• Developed an improved mutation operator, informed by the crossover matrix and a memory population, to guide the search.

Main Results:

• CCDE demonstrated significant improvements in generating high-quality solutions.
• The novel mutation strategy enhanced both exploration and exploitation capabilities.
• Tested on 30 benchmark and 5 real-world problems (CEC 2014 & 2011), CCDE outperformed other DE variants.

Conclusions:

• CCDE is an effective and simple DE variant for global numerical and engineering optimization.
• The proposed crossover matrix and memory-based mutation strategy enhance DE's performance.
• CCDE shows superior success rates in solving complex optimization problems compared to existing algorithms.